arises in many practical fields such as compressive sensing [1]}, [2]}, [3]}, signal processing [4]}, wireless communication [5]}, pattern recognition [6]}, to name a few.
In the model (REF ), \(\Vert \cdot \Vert _0\)  is often called the \(\ell _0\) -norm which counts the number of nonzero entries of a vector.
Depending on application, the function \(f(x)\)  may take different specific forms.
For instance, in compressed sensing scenarios, \(f(x)\)  is usually taken as \(\left\Vert y-Ax\right\Vert _2^2\)  which is an error metric for signal measurements.
The problem (REF ) is known to be NP-hard, and the main difficulty for solving this problem lies in locating the position of nonzero entries of a feasible sparse vector at which \(f(x)\)  is minimized.
